What you describe sounds like a fungal infection. To prevent the problem you'll need to spray your tree on a regular basis with a general-purpose fruit tree spray. This insecticide/fungicide combination is available at most garden supply stores. The general schedule is to spray at bud swelling, at petal drop and again about 10 days later.

It may be too late to spray your tree this year. If so, be sure to rake up the fallen leaves and make a note on your calendar to spray your tree early next spring.